Question

how do you solve cos^-1(sin(5pi/3)) without a calculator

Answer 1

Note that 5pi/6 is equal to 150 degrees
sin(150), is equal to sin (30) based on reference angle theorem. Also, based on 30-60-90 triangle, sin (30) = 1/2
cos^-1(1/2) is just like what angle, if cosined will result to 1/2. and that is equal to 60 degrees. :)

Answer 2

pi/6=30 degree
5*30=150degree
sin 150=1/2
cos^-1 (1/2)=pi/3

Answer 3

or 5pi/3

Answer 4

^ yeah, so it must be 60 or 150 degrees, in radians pi/3 or 5pi/3. :)

Answer 5

no no 60 or 300

Answer 6

\(sin\dfrac{5\pi}{3} = cos (\dfrac{\pi}{2}- \dfrac{5\pi}{3}) = cos (-\dfrac{7\pi}{6})\)